Math 4E03/6E03 Galois Theory

Instructor: Chung Pang Mok

Lectures: Monday, Thursday 9:30 - 10:20, Tuesday 10:30 - 11:20, HH 104

Office Hours: Monday, Thursday 3:00 - 4:00, HH 425

Email address: cpmok@math.mcmaster.ca

Topics to be covered

Basic theory of field extensions
Normal and separable extensions
The fundamental theorems of Galois Theory
Applications of Galois Theory, including solvability of algebraic equations by radicals
Galois Theory of Infinite extensions

Texts for the course

We will use the following for textbook:

A course in Galois theory. Cambridge University Press, by D.J.H.Garling.

Reference text which are recommended for the course are:

Fields and Galois Theory. By J.S. Milne. Available free of charge at

Abstract Algebra, 3rd edition, John Wiley. By Dummit and Foote.

Grading Policy

25% Homework

25% Mid-Term Test

50% Final

Assignments

Assignment 1: Due September 20th: Garling: p. 21: 3.3, p. 29: 3.15, p. 42: 4.1, p. 45: 4.5.

Assignment 2: Due September 27th: Garling: p.45: 4.6, p.47: 4.7, p. 48: 4.11, p. 52: 5.8.

Assignment 3: Due October 4th: Garling: p.53: 5.12, p.57: 6.6, p.59: 7.1, p.67: 7.4.

Assignment 4: Due October 11th: Garling: p.62: 7.2, p.70: 7.6, p.76: 8.5, 8.6.

Assignment 5: Due October 22nd: Garling: p.81: 9.6, 9.7

Assignment 6: Due October 29th: Garling: p.84: 10.1, p.86: 10.2, p.87: 10.4, p.90: 10.7.

Assignment 7: Due November 19th: Garling: p.94: 11.3, p.95: 11.6 a), c), p. 102, 12.1

Assignment 8: Due November 26th: Garling: p.124: 16.1, p.125: 16.4, p.128: 16.12, 16.13